头歌实践教学平台：三维图形观察OpenGL2.0

第3关：视口变换

一. 任务描述

1. 本关任务

(1) 理解视口变换的方法; (3) 根据视口变换的方法将viewport函数中的空白部分补充完整，并将main函数中的参数补充完整。

2. 输入

(1) 代码将自动输入一个边长为1的obj正方体模型，具体模型如下图：

(2) 视口矩阵中参数x、y的大小为宽度(width)的四分之一，参数w的大小为宽度的一半(width)，参数h的大小为高度的一半(height)，参数d=255。

3. 输出

具体结果如下图所示：

二. 相关知识

1.视口矩阵

将立方体[-1,1] * [-1,1] * [-1,1]映射到屏幕,得到立方体[x,x+w]* [y,y+h]* [0,d]。 这里d是z-buffer的分辨率，等于255，这样可以简单地转储z-buffer的黑白图像以便调试。 视口矩阵如下：

三. 操作说明

(1)按要求补全代码； (2)点击窗口右下角"测评"按钮，等待测评结果，如果通过后可进行下一关任务。

开始你的任务吧，祝你成功！

四、实验代码

#include <vector>
#include <cmath>
#include <algorithm>
#include <iostream>
#include "model.h"
#include "geometry.h"
#include "pngimage.h"

using namespace std;
const double PI = acos(-1.0);

void line(Vec3i p0, Vec3i p1, PNGImage  &image, PNGColor color)
{
	bool steep = false;
	if (std::abs(p0.x - p1.x) < std::abs(p0.y - p1.y))
	{
		std::swap(p0.x, p0.y);
		std::swap(p1.x, p1.y);
		steep = true;
	}
	if (p0.x > p1.x)
	{
		std::swap(p0.x, p1.x);
		std::swap(p0.y, p1.y);
	}

	int dx = p1.x - p0.x;
	int dy = std::abs(p1.y - p0.y);

	int y = p0.y;
	int d = -dx;
	for (int x = p0.x; x <= p1.x; x++)
	{
		if (steep)
			image.set(y, x, color);
		else
			image.set(x, y, color);

		d = d + 2 * dy;
		if (d > 0)
		{
			y += (p1.y > p0.y ? 1 : -1);
			d = d - 2 * dx;
		}
	}
}

Matrix viewport(int x, int y, int w, int h, int depth) {
	Matrix m = Matrix::identity(4);
	// Please add the code here
    /********** Begin ********/
    m[0][0]= w / 4.0 ;
    m[0][3]= w / 4.0 + x;

    m[1][1]= h / 4.0 ;
    m[1][3]= h / 4.0 + y;

    m[2][2]= depth / 2.0;
    m[2][3]= depth / 2.0;

	/********** End **********/
	return m;
}

Matrix lookat(Vec3f eye, Vec3f center, Vec3f up) {
	Vec3f z = (eye - center).normalize();
	Vec3f x = (up^z).normalize();
	Vec3f y = (z^x).normalize();
	Matrix res = Matrix::identity(4);
	for (int i = 0; i < 3; i++) {
		res[0][i] = x[i];
		res[1][i] = y[i];
		res[2][i] = z[i];
		res[i][3] = -center[i];
	}
	return res;
}

Matrix translation(Vec3f v) {
	Matrix Tr = Matrix::identity(4);
	Tr[0][3] = v.x;
	Tr[1][3] = v.y;
	Tr[2][3] = v.z;
	return Tr;
}

Matrix scale(float factorX, float factorY, float factorZ)
{
	Matrix Z = Matrix::identity(4);
	Z[0][0] = factorX;
	Z[1][1] = factorY;
	Z[2][2] = factorZ;
	return Z;
}

Matrix rotation_x(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[1][1] = R[2][2] = cosangle;
	R[1][2] = -sinangle;
	R[2][1] = sinangle;
	return R;
}

Matrix rotation_y(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[0][0] = R[2][2] = cosangle;
	R[0][2] = sinangle;
	R[2][0] = -sinangle;
	return R;
}

Matrix rotation_z(float angle) {
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
	R[0][0] = R[1][1] = cosangle;
	R[0][1] = -sinangle;
	R[1][0] = sinangle;
	return R;
}

int main(int argc, char** argv)
{
	const PNGColor white = PNGColor(255, 255, 255, 255);
	const PNGColor black = PNGColor(0, 0, 0, 255);
	const PNGColor red = PNGColor(255, 0, 0, 255);
	const PNGColor green = PNGColor(0, 255, 0, 255);
	const PNGColor blue = PNGColor(0, 0, 255, 255);
	const PNGColor yellow = PNGColor(255, 255, 0, 255);

	Model *model = NULL;

	Vec3f eye(0, 1.5, 4);
	Vec3f center(0, 0, 0);

	Matrix ModelView = lookat(eye, center, Vec3f(0, 1, 0));
	Matrix Projection = Matrix::projection(eye, center);


	const int width = 500;
	const int height = 500;
	const int depth = 255;
	// Please add the code here
    /********** Begin ********/
    Matrix ViewPort = Matrix::viewport(width / 4, width / 4, width / 2, height / 2, depth);

	/********** End **********/

	//generate some image
	PNGImage image(width, height, PNGImage::RGBA); //Error when RGB because lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size() in encode
	image.init(black);
	model = new Model("cube.obj");

	for (int i = 0; i < model->nfaces(); i++)
	{
		std::vector<int> face = model->face(i);
		for (int j = 0; j < (int)face.size(); j++)
		{
			Vec3f wp0 = model->vert(face[j]);
			Vec3f wp1 = model->vert(face[(j + 1) % face.size()]);

			Matrix S0 = scale(0.5, 0.5, 0.5);
			Vec3f swp0 = S0 * wp0;
			Vec3f swp1 = S0 * wp1;

			Vec3f sp0 = ViewPort*Projection*ModelView*swp0;
			Vec3f sp1 = ViewPort*Projection*ModelView*swp1;
			line(sp0, sp1, image, red);
		}
	}

	image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
	image.write_png_file("../img_step3/test.png");
	delete model;
	return 0;
}